A Scalable Approach for Variational Data Assimilation

D’Amore, Luisa; Arcucci, Rossella; Carracciuolo, Luisa; Murli, A.

doi:10.1007/s10915-014-9824-2

Cited by 29 publications

(39 citation statements)

References 26 publications

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“…In the following we let time t k be fixed, i.e. we consider the so-called 3D-Var DA problem [5], then for simplicity of notations, we refer to u b k and u DA k omitting index k.…”

Section: Definitionmentioning

confidence: 99%

“…Lions in 1988 [11]. In [1] the MPS is applied for solving a three dimensional variational Data Assimilation (DA) problem, which is a large scale inverse and ill posed problem used to handle a huge amount of data and requiring new mathematical and algorithmic approaches for its solution [2,3,4,5,6,9]. In this note, we review the two DD approches, namely the one introduced in [5] and the MPS method applied to 2 The DA inverse problem Let x ∈ Ω ⊂ R N , t ∈ [0, T ] and let u(t, x) be the state evolution of a predictive system from time t − ∆t to time t, governed by the mathematical…”

Section: Introductionmentioning

confidence: 99%

“…Since H is typically rank deficient and highly ill conditioned, DA is an ill posed inverse problem [5]. The objective is determine the solution in least squares sense.…”

Section: Introductionmentioning

confidence: 99%

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A note on domain decomposition approaches for solving 3D variational data assimilation models

D’Amore

Cacciapuoti

2019

Ricerche mat

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Data Assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state. This is a large scale ill posed inverse problem then in this note we consider the Tikhonov-regularized variational formulation of 3D-DA problem, namely the so-called 3D-Var DA problem. We review two Domain Decomposition (DD) approches, namely the functional DD and the discrete Multiplicative Parallel Schwarz, and as the 3D-Var DA problem is a least square problem, we prove the equivalence between these approches.the Euler-Lagrange equations arising from the VarDA minimization problem. We prove equivalence between these approaches. The note is organized as follows: in section 2 we briefly review DA inverse problem and its variational formulation [12]; in section 3 we apply the DD approches and we prove the main result.

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“…In the following we let time t k be fixed, i.e. we consider the so-called 3D-Var DA problem [5], then for simplicity of notations, we refer to u b k and u DA k omitting index k.…”

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A note on domain decomposition approaches for solving 3D variational data assimilation models

D’Amore

Cacciapuoti

2019

Ricerche mat

Self Cite

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“…Each blade consists of 2 Intel Xeon@2.33GHz quadcore processors sharing the same local 16 GB RAM memory for a total of 8 cores per blade and of 64 total cores. Here we do not provide scalability results as the computational model we are using is been already proved to be fully scalable [11]. All the routines we refer are implemented by using the Linear Algebra PACKage (LAPACK) library which provides a documentation and description of all the parameters [15].…”

Section: The S3dvar Computational Kernelmentioning

confidence: 99%

“…As claimed in [8], problem partitioning (decomposability: to break the problem into small enough independent less complex subproblems) is a universal source of scalable parallelism; the approach we use here meets the following demand: parallelization should be considered from the beginning [9,10]. In this work, we employ the algorithm in [11] which splits the DA problem (let us say, the global problem) into several DA problems which reproduce the DA problem at smaller dimensions (let us say, the local problems). Finally, the testbed we consider is a distributed computing environment.…”

Section: Introductionmentioning

confidence: 99%

Toward the S3DVAR data assimilation software for the Caspian Sea

Arcucci¹,

Celestino²,

Toumi³

et al. 2017

AIP Conference Proceedings

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Abstract. Data Assimilation (DA) is an uncertainty quantification technique used to incorporate observed data into a prediction model in order to improve numerical forecasted results. The forecasting model used for producing oceanographic prediction into the Caspian Sea is the Regional Ocean Modeling System (ROMS). Here we propose the computational issues we are facing in a DA software we are developing (we named S3DVAR) which implements a Scalable Three Dimensional Variational Data Assimilation model for assimilating sea surface temperature (SST) values collected into the Caspian Sea with observations provided by the Group of High resolution sea surface temperature (GHRSST). We present the algorithmic strategies we employ and the numerical issues on data collected in two of the months which present the most significant variability in water temperature: August and March.

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Parallel framework for dynamic domain decomposition of data assimilation problems: a case study on Kalman Filter algorithm

D’Amore

Cacciapuoti

2021

Comp and Math Methods

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We focus on Partial Differential Equation (PDE)-based Data Assimilation problems (DA) solved by means of variational approaches and Kalman filter algorithm. Recently, we presented a Domain Decomposition framework (we call it DD-DA, for short) performing a decomposition of the whole physical domain along space and time directions, and joining the idea of Schwarz's methods and parallel in time approaches. For effective parallelization of DD-DA algorithms, the computational load assigned to subdomains must be equally distributed. Usually computational cost is proportional to the amount of data entities assigned to partitions. Good quality partitioning also requires the volume of communication during calculation to be kept at its minimum. In order to deal with DD-DA problems where the observations are nonuniformly distributed and general sparse, in the present work we employ a parallel load balancing algorithm based on adaptive and dynamic defining of boundaries of DD-which is aimed to balance workload according to data location. We call it DyDD. As the numerical model underlying DA problems arising from the so-called discretize-then-optimize approach is the constrained least square model (CLS), we will use CLS as a reference state estimation problem and we validate DyDD on different scenarios.

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A Scalable Approach for Variational Data Assimilation

Cited by 29 publications

References 26 publications

A note on domain decomposition approaches for solving 3D variational data assimilation models

A note on domain decomposition approaches for solving 3D variational data assimilation models

Toward the S3DVAR data assimilation software for the Caspian Sea

Parallel framework for dynamic domain decomposition of data assimilation problems: a case study on Kalman Filter algorithm

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